Question

Determine whether the triangles are similar and justify your answer

Answer 1

a)

Answer:

Since the ratio of their corresponding sides are equal the two triangles are similar.

$\begin{gathered} \frac{AB}{BC}=\frac{15}{36}=\frac{5}{12} \\ \frac{XZ}{YZ}=\frac{10}{24}=\frac{5}{12} \\ \frac{AB}{BC}=\frac{XZ}{YZ}=\frac{5}{12} \end{gathered}$

Explanation:

Given the triangles in the attached image;

We want to confirm if they are similar.

For them to be similar the ratio of their corresponding sides must be equal.

$\frac{AB}{BC}=\frac{XZ}{YZ}=\text{ constant}$

Given;

$\begin{gathered} AB=15 \\ BC=36 \\ XZ=10 \\ YZ=24 \end{gathered}$

Substituting to get the ratio of the sides;

$\begin{gathered} \frac{AB}{BC}=\frac{15}{36}=\frac{5}{12} \\ \frac{XZ}{YZ}=\frac{10}{24}=\frac{5}{12} \\ \frac{AB}{BC}=\frac{XZ}{YZ}=\frac{5}{12} \end{gathered}$

Since the ratio of their corresponding sides are equal the two triangles are similar.